The graph of P(x)= a (x-b)(x+1)2(x-2) passes through (0,6). The value of b in the terms of a, is?

Q: The definition of the error function also defines an "error term" E(z, y). 15 Find E(x, y) for the f...

A: Given:    x^3 + y^3 = 15/56 xyz     Point : (8,7,57)

Q: Find the Laplace transform of: F (t) (2+t) e*. ( 3n.)! f(s) = + (s+4)* s+4 (s+4)3n+1 (3n)! f (s) = 2...

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Q: Evaluate the integral. 3x cos 2x dx O e3x [2 sin 2x - 3 cos 2x] + C 13 O 1 [2 e3x sin 2x + 3 cos 2x]...

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Q: Motion in Space: If 7(t) represents the position function, then the velocity function O = F"(t), the...

A: Position function of the particle is given by vector r(t)            Vector r(t) = 2√2*t i+e2t j + e...

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Q: polynomial P(x)= x3 + kx2+4x-12 has an x- intercept of -2.The polynomial can be written as P(x)=(x+a...

A: Given query is to find the value of c.

Q: a. Find the derivative of the vector function 7(t) = t+i+tj+tỉ. b. Use the result of part (a) to fin...

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Q: Consider the following function. 9(x) = x2/3 (a) If a + 0, find g'(a). g'(a) = (b) Illustrate that y...

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Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. dx =

A: Given: I=∫-∞-3e5x1+e5xdx   We know that; ∫1ax+bdx=1alnax+b+C

Q: 2. Evaluate the following integrals using partial fractions. 1 (a) / dx (x – 3)(x + 1)² (b) / 6х? + ...

A: We know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And ∫1ax+bdx=1alnax+b+C (a). Given: I=∫1...

Q: The roots of 6x² +7x + 34 = 0 are: Real and Equal Real and Distinct Complex and Unequal Imaginary an...

A: These questions  are related to algebraic operations, we will solve it using given information. 

Q: Which of the following differential equations can be solved with the substitution Y = VX? (6x + y ) ...

A: Any differential equation is solvable by y=vx if and only if it is homogeneous differential equation...

Q: . The equations x + y = 2 and 2x + 2y = 8 are examples of equations which are

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Q: Let S = {intersection of [2,4) and (3, 6]} union (4, 5). Determine Sup S. A.) 3 B.) 4 C.) 5 D.) 6

A: Given that:  S = {intersection of [2,4) and (3, 6]} union (4, 5)

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Q: P2.B: Evaluate the integral: (x+ 1)/2 J (x – 1)5/2

A: Evaluate the integral ∫x+112x-152dx

Q: the exact value of each trigonometric function  9. tan -30 degrees  15. tan 90 degrees  17. Sin 9...

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Q: Solve the following and show your complete solution Find Taylor Series Expansion and Compact form of...

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Q: (b) Find equations of the tangent lines at the points (1, 11) and (2, 12). y(x) = (at the point (1, ...

A: Part a,             y=8+5x2-2x3 and x=a

Q: Which of the following differential equations is exact? O (cos xy + xsiny) dx + (y – cos x + sin y) ...

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Q: 9.

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Q: After applying variation of parameters to y " +y = sec(x), the following equations are obtained c{ (...

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Q: Apple pies are often served with ice cream on top. If the pie is too hot, the ice cream will melt to...

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Q: (3) 3x²y² + 2x³y = 0

A: Follow the procedure given below.

Q: Find the derivative of the function using the definition of derivative. f(x) = 3 + 6x – 8x² f'(x) = ...

A: Given, f(x)=3+6x-8x2 Domain of f(x)=(-∞,∞)

Q: y" -y + 2x t2 where: a (0) = a' (0) = 0 %3D y (0) = y (0) = 0 Find: L (y) L (y) 293 s+2 - OL (y) = 2...

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Q: The differential equation y" – 4y = e2t has a particular solution of the form yp = uje + uze2t. dui ...

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Q: A 2-lb-per-gallon salt solution is pumped in a 400-gallon tank at a rate of 2 gallons per minute. At...

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Q: Fill in the blank with the appropriate word, phrase, or symbol. In the expression 5-/7, the 7 is cal...

A: We have,

Q: A spring is stretched 3 in. when an 8-lb weight is hung on it. The 8-lb weight is attached and pushe...

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Q: To make a potato salad, a chef cooked some unpeeled potatoes in boiling water at 100°C. Once the pot...

A: The correct answer is option (A) i.e. t = 11.4 minutes

Q: 20-sin 20 Find the maximum value of the function 02

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Q: Applying variation of parameters to the DE: y" - y = e +e ,we get the following system of equations:...

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Q: (2x - 3 if x0 Sketch this graph on the grid below. Is this function discontiruous? Tf yes, state whe...

A: The given function is,f(x)=2x-3if x≤02+x2if x>0

Q: |(cos? x – sin² x + 1) sin x cos x dx

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Q: (5an 20 elan 20 sec²2 Bd ß 1. e?x +2e* dx e* +1 2.

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Q: Compute / 7(t)dt for 7(t) = (t – 2t, 7, cos (2t)) %3D А. 1 sin В. B. G*-t, 7, sin (2t) ) + č С. tA –...

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Q: Solve the differential equation with appropriate method. Finalize answer in terms of x and C combine...

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Q: A small metal bar, whose initial temperature is 40°C, is dropped into a container of boiling water w...

A: Follow the procedure given below.

Q: A stream containing 80 grams per liter of a dye is pumped into a mixing tank with 400 liters of fres...

A: The answer is 32kg

Q: Determine whether the number is rational or irrational. 3.789778977789.. Is 3.789778977789... ration...

A: The given number is: 3.789778977789...

Q: BASIC PROPERTTES OF INTTE RATION IHTEGRATE THE FOllowING:

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Q: Subtract. Simplify by collecting like radical terms, if possible. 7/7- 11/7 7./7 - 11/7 =O (Type an ...

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Q: 1419857* 4913*

A: We know that, ∫axdx=axlna+C And The exponent rule: anbn=a×bn   Given: I=∫1419857x4913xdx

Q: Find the L{y(t)}, given the initial value proble y" - 3y' + 2y = t - 2;

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Q: iven the differential equation dæ? dy - y = cosh(x) + x ropose an appropriate particular solution. Y...

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Q: (4) t(s² + t²)ds – s(s² – t²)dt = 0

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Q: Given the differential equation: y"+3y'- 4y = e42 Propose an appropriate particular solution Yp = (A...

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Q: Which of the following equations can be solved using the method of undetermined coefficients?

A: Given that: 1. y''+6y'+9y=xcosx2. y''+4y'+5y=5x-2sinx3. y''+3y'+2y2=2xcos(3x)

Q: form of the piecewise function: 0 st<3 t2 3 1 ste-3s s2 3 4 te-3s s2 6.

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